Core or not, you are right that Hyper-V does not currently support USB passthrough. However, we are still able to communicate directly to USB device connected to the physical machine that through our "backup repository" component. As I've mention, we do support installing this component on core server.
It will be more clear for you once you setup our product and look at our Backup Repositories. Essentially, they virtualize access to any storage on any server for our backup engine. Just pick your physical server in question, pick the USB drive volume on that server, and make it your backup repository. After that, any backup job will be able to write data there directly. Very simple yet powerful concept.